Method for determining sedimentary rock pore pressure caused by effective stress unloading

ABSTRACT

An improved technique to more accurately calculate pore pressure of sedimentary rock due to subsurface fluid expansion where the technique is built upon a combination of known force balanced in situ loading limb mineralogical stress/strain relationships with locally variable unloading stress/strain relationships, including that in stress/strain space, the material properties governed loading limb is an upper limit for the many possible unloading limbs; also, a method for relating these different natural stress/strain paths and applying the correct path to calculate pore fluid pressure from in situ force balance is disclosed such that the method is preferably calibrated with in situ stress/strain data which allows for a lithologic sealing caprock to be identified and the locally prevailing in situ unloading limb stress/strain relationship to be estimated, where the forced balanced loading and unloading calibrations are applied to more accurately determine well casing depths using either wireline or real-time &#34;measured while drilling&#34; petrophysical data; and also solidity (1.0--Porosity) is the in situ parameter of choice which can be measured petrophysically in the borehole, where pore pressure is the fraction of the total external load which is borne by the fluids in the pore space of a sedimentary rock, and the solid framework of a granular sedimentary rock bears the force balance remainder of the external confining load as effective stress; so that loading and unloading power law linear stress/strain relationships are determined between effective stress and solidity for common sedimentary rocks.

BACKGROUND OF THE INVENTION

1. Field of Invention

The present invention relates to an improved method for determining thepressure of fluid contained in a sedimentary rock. A mineralogicallygeneral force balanced stress/strain--loading limb relationship is astarting point. This relationship is defined in U.S. Pat. No. 5,282,384to Holbrook, assigned to the assignee of the present invention, andwhich is incorporated herein by reference, which discloses how tocalculate sedimentary rock pore pressure when the effective stress loadis either constant or increasing and also teaches how the minimumprincipal stress and fracture pressure also can be calculated from insitu strain data in Normal Fault Regime ˜biaxial basins. Fracturepressure and pore fluid pressure are the safe force balance boreholefluid pressure limits for drilling the uncased (open to the surface)portion of a borehole into the subsurface.

Well after these loading limb open borehole force balance relationshipswere disclosed in the prior Holbrook patent, an extended set of forcebalanced Earth in situ stress/strain inter-relationships was discovered.These Earth in situ force balance inter-relationships can be applied tofurther improve the drilling decision making process. This newlydiscovered Earth in situ force balance inter-relationship, led to adirect force balance means of determining the physical location andpressure upper limit of fluid expansion generated pore fluid pressure.The methods disclosed in this invention produce further valuablegeological information from in situ petrophysical measurements which isuseful in the hydrocarbon recovery industry.

2. Background

Pore fluid pressure and fracture pressure are the most importantexternal geologic factors affecting the safety and cost of drilling ofan oil well. Exceeding either in situ force balance limit in an openborehole frequently leads to dangerous and usually costly well controlproblems. The borehole fluid hydrostatic pressure (Pb) must be greaterthan the formation pore fluid pressure (P_(p)) if one is to avoid therisk of a possibly catastrophic blowout. Likewise, the borehole fluidcirculating pressure must be less than the fracture propagation pressure(Pf) if one is to avoid the risk of lost circulation.

Several expensive casing strings are usually required so that an oilwell can be drilled within the limits of the open borehole pore fluidpressure and fracture propagation pressure limits. Great savings wouldbe realized during well planning if one or more casing string could beeliminated through better pore pressure and fracture pressure knowledge.The present invention also enhances the safety of oil or gas welldrilling operations. Presently, a considerable portion of expensive rigtime is spent in a remedial fashion dealing with unexpected porepressure and fracture pressure problems encountered while drilling. Theimproved information from this invention should significantly reducedrilling operations costs by reducing the number of these dangeroussituations.

Because of the critical relationship to drilling operations, there arenumerous techniques for calculating pore fluid pressure. All knownpetrophysical prior art methods calculate pore fluid pressure indirectlybased upon measured rock properties. Most of these methods follow acalibration procedure which is not based on mechanical or physicalinformation. Instead, these calibration procedures are generally basedupon the extension of an observed empirical relationship between ameasured physical parameter and a "normal" or hydrostatic compactiontrend. The empirical "normal" trend line (Pn) is the average value ofthe measured parameter which changes as a function of depth.

The change in the measured parameter (Pn) as a function of depthaccording to these prior art techniques is indirectly related to achange in compaction of the sedimentary rock. The measured parameterdescribed in a pressure prediction technique is usually not compactionalstrain. The method operator in charge of pore pressure prediction mustthen decide whether the extrapolated "normal" compaction vs. depth trendline being used is correct or not using some non-physical interpretivebasis. Direct empirical (i.e. non-physical) relationships have been theonly pore pressure prediction techniques used by the oil industry untilvery recently.

Sedimentary rocks are compacted by the effective stress applied to theirgrain matrix framework. When fluid pressure is approximately hydrostaticand the overburden is gradually increasing, both depth and effectivestress are increasing. Under these conditions, depth behaves as apseudo-stress variable. However, when pore pressure is elevated,effective stress and overburden gradients can be either increasing ordecreasing and depth is not a pseudo-stress variable.

Most of the prior art methods for determining pore fluid pressure usedepth as a pseudo-stress variable in both "normal" and "excess"pressured intervals which results in significant pore pressurecalculation errors. The potential for this error when using anon-physical velocity-depth trend line method will be illustrated laterin reference to the patents to Kan et al.

Another significant failing of most prior art pore pressure calculationtechniques is attributable to their basic formulation. According toprior art depth trend techniques, pore pressure (P_(p)) is calculated asa sum of "normal" hydrostatic fluid pressure which is inferred from anextended compaction-depth trend; plus a differential or "excess" fluidpressure (ΔP) which is related to a measured difference from the"normal" trend. The (ΔP) calibration or correction term is backcalculated after the fact from measured pore pressures in a nearby wellor group of wells within a local area. The equation expressing thisnon-physical local calibration relationship is:

    Pp=Pn+ΔP                                             (1)

where Pp is the pressure of fluid in the pore space of rock, Pn is theempirical calculation of the normal pressure trend line and ΔP is thedifference in pressure from the normal pressure trend line.

Equation (1) is not a physically representative mathematicalformulation. Pascal's Principle requires that all of the fluids in agiven local pore space or container be at the same pressure. Physicallyspeaking, "excess" pressure cannot and does not exist in a pore space.Since the "excess" pressure term (ΔP) does not exist in nature, "excess"pressure cannot be physically related to any measured parameter.Calibrating a measured physical parameter to a quantity which does notexist, i.e. (ΔP), has been an acceptable engineering shortcut for a longtime. The penalty when applying this (Pp=Pn+ΔP) shortcut method is thatthe results are specific to the calibration area and the fluidpressurization mechanism in that particular field or reservoir. "Normalcompaction trend" operators usually do not know the fluid pressurizationmechanism, nor can they change their procedure to account for themechanism. The (ΔP) calibration is fundamentally non-physical and notrelated to the known loading and unloading stress/strain relationshipsof sedimentary rocks. As these stress/strain relationships are sodifferent, there is great risk in mis-applying an empirical (Pp=Pn+ΔP)relationship which contain no means of determining stress paths.

U.S. Pat. No. 5,081,612 to Scott et al discloses a method fordetermining formation pore pressure from remotely sensed seismic data.This particular method depends upon a hydrostatically compactedreference velocity vs. depth (Pn) profile. Referring back to Equation 1,this profile is essentially an observed or inferred curved (Pn) velocitygradient. The Scott et al pore pressure gradient technique applies toshale, which is also common to most of the prior art methods using a(Pp=Pn+ΔP) formulation. Pore pressures are calculated with respect tothe reference velocity vs. depth trend line which is an indirectviolation of Pascal's Principle.

In U.S. Pat. Nos. 5,130,949 and 5,233,568 to Kan et al, like U.S. Pat.No. 5,081,612 to Scott et al, the basic pore pressure prediction methodis also based upon a velocity vs. depth compaction trend line. Kan etal's FIG. 5 demonstrates the historically common but physicallyincorrect (Pp=Pn+ΔP) methodology. The normal compaction trend lineinterpreted from the hydrostatic zone is shown on FIGS. 5b and 5d. Thelowest hydrostatically compacted data point is slightly above 5,000feet. The extrapolated (Pn) interval transit time-depth trend linedecreases by half continuously every 8,000 feet on the logarithmictransit time scale shown.

The extrapolated empirical (Pn) shale transit time--depth trend line isbeyond any possible physical reality at 8,000 feet or essentially 3,000feet into the overpressured zone. Shales can compact no further thanzero porosity which corresponds to a transit time of about 90microseconds/foot. In regions that are more nearly hydrostatic than theexample shown in reproduced FIG. 5, the 90 microseconds/foot shaletransit time limit is not reached at depths above 20,000 feet.

The calibration within the (Pn) hydrostatic zone above 5,000 feet isreasonable. The projection to 90 microseconds/foot 3,000 feet below topof overpressure is physically unreasonable. Quartz is the mostcompaction resistant sedimentary mineral. The extrapolated (Pn) trendpasses the zero porosity quartz transit time of 56 microseconds/foot atabout 14,000 feet. The transit time of the Mohorovic discontinuity belowthe base of the Earth's crust is about 37 microseconds/foot. The (Pn)trend line is 37 microseconds/foot at 19,000 feet and continues toincrease below. The actual depth of the base of the crust is about100,000 feet on average, not 19,000 feet which is extrapolated from theinterpreted normal shale compaction (Pn) depth trend of FIG. 5 of Kan etal.

The extrapolated (Pn) trend is grossly off compared to known transittime limits below the hydrostatic zone. Applying the (Pp=Pn+ΔP)methodology the known error in the projected (Pn) depth trend is forcedinto the (ΔP) term which is calculated by difference. Thus, thephysically unreasonable (Pn) trend is automatically compensated for bythe physically invalid (Pn+ΔP) formulation relied upon for calibration.In fact any combination of (Pn+ΔP) is forced to the correct answer bythe measured pore pressure (Pp) in a calibration well. It takes twoequal and opposite wrongs; one physically unrealistic (Pn), and onephysically invalid (ΔP) to make a right (Pp). Whenever the extrapolated(Pp=Pn+ΔP) trend line methodology is reported to have been successfullyapplied; it signifies only that a force balance (ΔP) correction has beenapplied to a frequently erroneous extrapolated (Pn) trend line.

All of the extrapolated (Pp=Pn+ΔP) trend line methods suffer from thesame non-physical (Pn) extrapolation which is transparent to theoperator after the local calibration is made. The calibrations have onlylocal applicability because you get a different extrapolated (Pn) trenddepending upon where the base of the hydrostatically compacted depthinterval occurs. In any particular area many other physical factors, forexample overburden gradient, that exist affect the empirical calibrationat that depth but are not accounted for in the empirical short cutmethodology.

There are at least three (3) prior art methods for determining porefluid pressure from petrophysical measurements which are based upon theeffective stress law. A one-dimensional gravitational force balance waselucidated by Terzaghi, in his 1941 article entitled "Undisturbed ClaySamples and Undisturbed Clays", discussing compaction studies of marinesediments. Terzaghi first presented this uniaxial force balanceequation;

    Pp=S.sub.v -σ.sub.v                                  ( 2)

This relationship states that the fluid pressure in the pore space (Pp)can be calculated as the difference between the overburden load (Sv) andthe vertical load borne by the sediment grain--grain contacts (σ_(v)).In the science of rock and soil mechanics, this (σ_(v)) term is known asthe effective vertical stress.

U.S. Pat. No. 5,200,929 to Bowers is based upon in situ empiricallydetermined velocity vs. calculated effective stress relationships. Ituses the Terzaghi uniaxial Equation (2) to calculate effective stress.In NFR˜biaxial basins the uniaxial calibration is coincidentally relatedto average effective stress force balance which directly causes theobserved sediment compaction. This method accounts for both the loadingand unloading stress/strain relationships of sedimentary rocks. Themethod is intended for use only in velocity reversal zones where fluidexpansion unloading is the known fluid pressurization mechanism. Themethod is dependent only on velocity measurements which are indirectlyrelated to strain and lithology.

The Bowers method is a significant technical advance because it uses auniaxial approximate measure of effective stress and for its recognitionof stress/strain hysteresis in sedimentary rocks. However, like thepreviously described pore pressure methods, the Bowers method alsodepends upon local empirical-velocity calibration to determine thecoefficients for all its calibration and pore pressure predictionrelationships.

Using in situ velocity vs. effective stress data for shales only, Bowersdescribes a method for defining the shape of loading and unloadingeffective stress-shale acoustic velocity curves. His "virgin curverelationship" is portrayed as the solid line on Bower's FIG. 4. Thiscurve corresponds to a loading limb stress/strain relationship withshale velocity being the indirect measure of strain.

At present the shale velocity-strain relationship is still poorly known.The velocity of an individual shale sample varies by up to 25% dependingon whether the measurement is made parallel or perpendicular to bedding,as discussed in a 1994 article by Sayers, entitled "The ElasticAnisotropy of Shales". An in situ measurement of velocity on shales withidentical strain would produce very different pore pressure answersdepending on the formation dip at the measurement location.

FIG. 4 of the Bowers patent shows how the extension of local empiricalvelocity loading limb and unloading limb relationships intersect. Theposition of this intersection point in both depth and effective stressspace has a major impact on the value of the unloading limb calculatedpore pressure. The data from both loading and unloading limbs must beknown and their curving functions determined through interpolationbefore their intersection point can be determined by extrapolation. Noother means for establishing the onset of unloading limb pore pressureis revealed by Bowers. If this method were to be applied with real-timeMeasurement-While-Drilling data, one would not have a criterion todetermine where and when to switch from loading to unloadingstress-velocity relationships.

U K Patent No. 2,174,201A to Fitzgerald reveals a commonmisunderstanding with respect to the interpretation of laboratory vs. insitu stress/strain relationships. Fitzgerald's method is based upon two(2) linear acoustic velocity vs. stress relationships observed in two(2) shales in a laboratory. Virtually all observed laboratorystress/strain relationships occur along the dominantly elasticunloading-reloading stress path of a rock sample. These rock specificstress paths intersect a mineralogy specific loading limb stress path atthe point of maximum effective stress loading. There is no clearindication apparent during laboratory experiments on relatively hardrocks when or where the hysteresis join point is reached. The slopes ofthe initial loading vs. unloading-reloading limbs are very different.

Fitzgerald's patent indicates a lack of awareness of stress/strainhysteresis in sedimentary rocks and makes calculations based only uponthe unloading-reloading stress path. In Fitzgerald, the key rockdescription qualifier "known constitution" is entirely appropriate andcorrect. For this method to operate as described a huge catalog of"known constituent" sedimentary rocks would have to be provided toappropriately match stress paths. Only two (2) rock stress paths aredescribed. Fitzgerald describes three (3) empirical stress pathcoefficients which would need to be established to have a predictiveequation. These coefficients could not be established without the "knownconstituent" rock sample or its equivalent from a rock sample catalog.The Fitzgerald patent is operative only for the two (2) rocks describedand could not be generalized into a general subsurface pore pressurepredictive method.

U.S. Pat. No. 5,282,384 to Holbrook applies force balance for porepressure prediction using a power law effective stress/strain compactionfunction. The key scientific elements to this methodology and approachare:

1. The use of the uniaxial Terzaghi force balance (Equation 2) in˜biaxial Normal Fault Regime Basins.

2. The correlation of effective stress to solidity (1.0-φ, where φ isporosity) which is a direct measure of in situ strain for granularsolids. One skilled in the art will recognize the substitution of therelationship (φ/1.0-φ).

3. The discovery through this application that both vertical effectivestress and the effective horizontal/vertical stress ratio in ˜biaxialNormal Fault Regime basins are directly related to in situ strain in alllithologies and at all depths.

These direct stress/strain relationships are related to sedimentary rockmineralogy and expressed quantitatively as Equations 6, 7, and 8 in theHolbrook Pat. No. 5,282,384. These equations and empirical coefficientsdescribe a complete three-dimensional grain and fluid force balance.Additionally, the equations in the patent explain why and how theuniaxial Terzaghi force balance works in ˜biaxial Normal Fault Regimebasins where horizontal effective stresses are known to increase withdepth. Further, lithologic and stress technical support for the patentedmethod are described in articles by Holbrook in 1995, "The RelationshipBetween Porosity, Mineralogy, and Effective Stress in GranularSedimentary Rocks", and 1996, "The Use of Petrophysical Data for WellPlanning, Drilling Safety and Efficiency" and "A Simple Closed ForceBalanced Solution for Pore Pressure, Overburden, and the PrincipalEffective Stress in the Earth".

There are severe calibration problems with all of the (Pp=Pn+ΔP) priorart empirical pore pressure prediction methodologies described above.Most of the prior art acoustic pore pressure prediction methodologiesuse the same non-physical relationship (Equation 1) and suffer the samegeneral pore pressure calibration-prediction problems. The calibrationsfor all these methods, even including Bowers' (Equation 2) empiricaleffective stress-velocity relationships apply only locally. Thefundamental problem with all the other prior art methods is that of theunspecified relationships between stress and strain. Holbrook (Equation2) is the only prior art pore pressure method which embodies a directphysical in situ stress/strain calibration basis.

Articles by Ward et al in 1994, "The Application of Petrophysical Datato Improved Pore and Fracture Pressure Determination in North Sea GrabenHPHT Wells", and 1995, "Evidence for Sedimentary Unloading caused byFluid Expansion Overpresssure-generating Mechanics", point out evidencefor fluid expansion generated fluid overpressuring which was directlyrelated to in situ measurable strain (solidity). The unloading limbstress/strain (solidity) data plotted in a very different areas are ingeneral agreement with Bowers' "virgin curve" vs. unloading velocitydata. Ward et al's FIG. 2 from their 1994 article illustrates thesimilarities, differences, advantages and implementation problemsassociated with applying unloading stress/strain relationships to theproblem of pore pressure determination.

The Ward et al FIG. 2 loading and unloading limb relationships are powerlaw linear stress/strain functions. The major significant advantages ofthis over the Bowers calibration are that: 1) effective stress isdirectly related to in situ strain; and 2) the power law function islinear, not curved, which makes calibration, interpolation andextrapolation much more simple and reliable. FIG. 4 of Bowers and FIG. 2of Ward et al are geometrically similar. Bowers' shale velocity curveswould approximate Ward et al's power law linear stress/strain functionsif the appropriate material properties transformations were made. Theinterpretation calibration step and the pore pressure prediction stepare much easier to accomplish and more accurate when using the forcebalanced power law linear relationships.

Ward et al points out in their FIG. 3 that there are many possibleunloading stress/strain relationships related to the loading limbrelationship depending on the last peak effective stress loading. Theinterpretive definition of this loading limb intersection point is acritical problem here as it was in the Bowers' methodology.

Ward et al, in the 1994 article, made some observations which areillustrated as FIGS. 3 and 4 which are coincidentally related to aphysical rock properties means of determining the loading vs. fluidexpansion unloading intersection point in the subsurface. The depthrange of a low porosity vertical seal is shown on the FIG. 3 geologiccross section. Pore fluid pressure gradient as indicated by the heavycurved lines on the figure increases dramatically somewhere within thelow porosity seal zone. The onset of fluid expansion unloading probablyoccurs somewhere in the low porosity seal zone which can be recognizedfrom petrophysical measurements. This relationship is discerned mainlyby inference from the markedly different observed pressure gradientsabove and below the low porosity seal zone. Low porosity is a propertyof the seal zone, but it does not capture or quantify the actualpressure seal relationship.

Ward et al's 1994 article FIG. 5 is a generalized pressure profileshowing the relationships between disequilibrium compaction fluidpressurization mechanisms and fluid expansion pressurization mechanisms.The low porosity vertical seal within the chalk is also shown on thisdiagram. Supporting this circumstantial evidence are the calculations ofwhich indicated that a very low permeability seal is needed for thefluid expansion pressurization mechanism to be operative.

Gaarenstroom et al, in a 1993 article entitled "Overpressures in theCentral North Sea: Implications for Trap Integrity and Drilling Safety",also demonstrate a reasonable partial understanding of the relationshipsthat govern pore fluid pressure in the subsurface. Gaarenstroom et alrelate trap integrity to formation strength. While a certain minimumformation strength is required, it is not strength that is regulatingthe compartment pressure. Very weak shales, salt, as well as very strongimpermeable quartzites have very different strengths. All thesedifferent strength lithologies can equally well accomplish the job ofsealing a pressure compartment as long as they have sufficiently lowintergranular permeability.

FIGS. 3 and 4 of the Ward et al 1994 article show the transition betweenloading and unloading limb stress/strain relationships is related to alow porosity zone within the North Sea chalk interval. The transitionbetween effective stress loading and unloading occurs in this zone. Thezone definition is broad and general and does not specify the sealingmechanism or exactly where the seal is located within the low porosityzone. The difference between Ward et al's description and the presentinvention is that low porosity is coincident with, but is not equal tohigh fracture pressure. A low porosity rock will have different fracturepressures which also depend upon vertical effective stress and porepressure. Fracture pressure is the actual force that holds the in situCompartment Pressure Limit Valve closed.

Ward et al and Gaarenstroom et al have identified two (2) differentfactors, strength and low porosity which are coincidentally related tofracture pressure under special circumstances. Methods related to theseparameters should work in a relative sense under the particular geologicsituation they describe. The distinction made here is that when fracturepressure is used as the discrimination parameter, the method works ingeneral because of force balance regardless of these othercircumstances.

The relationships described by Gaarenstroom et al, Bowers and Ward et alindicate that they have a general understanding of the factorscoincidentally related to the occurrence of pressure compartments, andloading vs. unloading stress/strain relationships. The caprock sealrequired for unloading can be recognized as a relative porosity lowwithin a sequence as described by Ward et al. Porosity provides a meansfor recognizing a compartment pressure seal under the specified averageregional conditions. But porosity does not provide the means forquantifying the caprock's pressure sealing capacity which controls thepore pressure below.

Seal pressure capacity is the truly important aspect of pore pressureforecasting ahead of the bit. Gaarenstroom et al describe rock strengthrelationship is likewise a related seal recognition criteria which lacksthe means for seal capacity quantification. The solution to theseproblems lies in the seal mechanism which is not identified in the priorart.

SUMMARY OF INVENTION

The present invention provides an improved technique to more accuratelycalculate pore pressure of sedimentary rock resulting from subsurfacefluid expansion.

There is a static force balance between the total external load appliedto a subsurface sedimentary rock and the grains and fluid which composethat rock. All of the external load, which can be described as three (3)principal external confining stresses (S_(AVE)), is borne by the solidand fluid which compose a sedimentary rock. The fluid in the pore spaceof a sedimentary rock supports its portion of the external loadisotropically as a pore fluid pressure (Pp). The solid grains of asedimentary rock support the remaining external load which is calledeffective stress (φ_(AVE)). The solid phase can support some level ofanisotropy between the three (3) principal stresses. Even if the levelsof the three (3) principal stresses are not known; the static balancebetween external (S_(AVE)) and internal (Pp+σ_(AVE)) forces is known tobe equal as demonstrated by the effective stress theorem in the 1980article by Carroll, entitled "Compaction of Dry or Fluid Filled PorousMaterial".

The solid portion of a sedimentary rock is composed almost entirely of afew simple minerals. Each mineral is a crystalline structure having anordered spacing of ions, and a narrowly fixed chemical composition. Theeffective stress load is ultimately borne by the mineral ionic bonds.Average ionic bond strength is the main factor controlling the physicaland chemical properties of minerals. Knowing the mineralogic compositionof a sedimentary rock, places narrow limits on a host of useful relatedrock physical and chemical properties including compaction resistanceand rock strength.

Solidity is the complement of porosity ((1.0-φ)=solidity). Solidity is avery important rock physical property which is also a direct measure ofcompactional strain for sedimentary rocks. The choice of solidity as thestrain definition in conjunction with force balance stress definitionsis a particularly useful though hardly used frame of reference in rockmechanics. This combined rock property (solidity=total in situ strain)frame of reference gains one a degree of freedom on many rock and soilmechanics problems. Many rock mechanics interrelationships that haveotherwise required measurement control are therein controlled bydefinition.

The required elements for this new technique are either force balancedefinitions, material properties definitions, or strain definitions uponwhich an in situ pore pressure prediction methodology can be built asdiscussed in the 1996 article by Holbrook. These definitions provide thebasis for a rock mechanics system which depends only upon in situpetrophysical and borehole fluid pressure measurements. Stress andstrain (solidity) are related through force balance and composition(mineralogy), all of which are indirectly measured in situ withcalibrated petrophysical instruments.

There are two (2) significant new developments which are built upon U.S.Pat. No. 5,282,384 to Holbrook. There is an internally regulatinginteraction between the two (2) force balance variables, fracturepressure and pore pressure in the subsurface. This relationship is an insitu relative force balance corollary to the basic force balance methodsdisclosed in the above patent.

Identifying a quantifiable force balance seal mechanism is the firststep to a more general solution as to when and where to switch betweenloading limb and unloading limb stress/strain relationships. A forcebalanced in situ petrophysical measurement adaptive method fortriggering the switch is disclosed in this patent. The unloading limbstress/strain relationship is calculated from a calibration well triggerpoint. The adaptive method assures consistent trigger point placementbetween planning and drilling wells. The planning well measuredunloading limb stress/strain relationship is applied from the drillingwell trigger point for pore fluid prediction within a fluid expansionunloading compartment.

The maximum compartment pore fluid pressure limits can also becalculated indirectly from related in situ force balance relationshipsat the trigger point when the sealing mechanism is known. The new methodinvolves a mechanism dependent transfer of mechanically sensible in situstress/strain relationships from planning or drilling well in situpetrophysical measurements. The compatible methods for force balancedpore pressure calculation and underlying compartment upper fluidpressure limits will be described below.

Fracture pressure at the free water level of a reservoir is the upperfluid pressure limit for the relative hydrostatic pressures within acontinuous reservoir compartment. By projecting caprock physical rockproperties and overburden to the free water level, one can thereafterpredict the pore fluid pressure limit for the entire pressurecompartment using Pascal's Principle. At great depth and in the presenceof fluids that have significant thermal expansion potential, mostcontinuous pressure compartments are at this pressure limit.

These and further objects, features and advantages of the presentinvention would become apparent from the following detaileddescriptions, wherein reference is made to the Figures n theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 graphical represents the power law linear loading and unloadingin situ stress/strain relationships for shale formations.

FIG. 2 illustrates a continuous fluid pressure compartment having anatural fracture system, caprock Minimum Work Fracture Pressure limitfor the pressure compartment, and representative force balanced in situRock Mechanics System continuous logs.

FIG. 3 is a program flow chart to identify pore pressure increasesassociated with possible local sealing fracture pressure maxima.

FIG. 4 is a program flow chart to identify the maximum expected porepressure in a continuous fluid pressure compartment.

FIG. 5 is a program flow chart to calculate pore pressure usingunloading stress/strain relationships.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

U.S. Pat. No. 5,282,384 to Holbrook, which is incorporated herein byreference, is a complete and accurate description of the method tocalculate sedimentary rock pore pressure and fracture pressure in NormalFault Regime-biaxial basins under loading limb stress/strain conditions.In ˜biaxial NFR basins, the maximum principal and effective stresses arevertical; and the two (2) horizontal stresses are approximately equal.The compactional calibrations in this method are derived from in situloading limb stress/strain (solidity) relationships as discussed in the1995 article by Holbrook previously mentioned herein. Vertical and thetwo (2) approximately equal horizontal effective stresses are related tosolidity in these basins as described by Equations 6, and 8 of U.S. Pat.No. 5,282,384. Overburden (Sv) and effective vertical stress (σ_(v))differ by pore fluid pressure (Pp). This is Terzaghi's uniaxial forcebalance effective stress law (Equation (2) herein) which iscoincidentally proportional to total stress in NFR ˜biaxial basins. Morethan half of the world's sedimentary basins have ˜biaxial NFR stressfields.

A closed form force balanced stress/strain relationship exists in NFR˜biaxial basins as described in the 1996 article by Holbrook, becauseall three (3) principal stresses are directly related to the samemeasure of volumetric strain (solidity). Sedimentary rocks are mixturesof mineral grains. Only two (2) coefficients (α, and σ_(max)) arerequired to relate volumetric stress to strain. These coefficients canbe calculated using Equations 4, and 5 of U.S. Pat. No. 5,282,384 as amineralogically weighted average for all sedimentary rocks as discussedin the 1995 article by Holbrook. The effective stress loading limbrelationship for a sedimentary rock of any mineralogic composition isdescribed as Equation 6 of that same patent. U.S. Pat. No. 5,282,384 isthe preferred embodiment for obtaining the force balance variables; 1.overburden, 2. effective vertical stress, 3. pore fluid pressure 4.effective horizontal stress, and 5. fracture propagation pressure. Thesevariables are related through force balance in ˜biaxial NFR basins andthis natural physical constraint offers many advantages over any otherprocedure for arriving at the same five (5) variables.

All the other prior art pore pressure and fracture pressure methodsdepend indirectly on these five (5) physical variables in one way oranother. This preferred embodiment description is not meant to excludeany other means of approximating these five (5) variables under anybasin or location specific conditions. The reason U.S. Pat. No.5,282,384 is preferred is that it is exactly physically representative.The known force balanced interdependence of all five (5) variables is apowerful boundary condition which is applicable to location specificconditions within ˜biaxial Normal Fault Regime Basins.

The preferred procedure for defining an unloading limb stress/strainrelationship is to relate it to the appropriate loading limbstress/strain relationship, ie. Equation 6 of U.S. Pat. No. 5,282,384.The many possible unloading limb stress/strain relationships shown onFIG. 1 as 10, 11, 12 and 13 can also be expressed as power law functionslike Equation 6. At geologic loading rates the loading limb 14 is aphysical upper limit to the unloading-reloading limb. Starting from anyunloaded point under the loading limb 14 portrayed on FIG. 1, areloading limb stress/strain path (for example dashed line 10) will befollowed until the loading limb envelope is reached, as defined byEquation 6. Further, additional loading will follow the solid Equation 6loading limb stress/strain path 14 toward the (σ_(Max)) total solidityintercept.

The preferred point of departure or reattachment of an unloading limb,for example 10, to the loading limb 14 depends upon a physical mechanismin the subsurface. Under most circumstances thermal or hydrocarboncracking fluid expansion mechanisms produce relatively small volumes offluid. A very efficient seal is required for this small fluid volume tosignificantly raise the fluid pressure of a large volume continuousfluid pressure compartment. The high fluid pressure seal must becontinuous and unbroken over the top of the compartment in order to bean effective seal. Within a single observation well, a local point ofmaximum pressure sealing efficiency (low intergranular permeability andhigh fracture pressure) would be part of the required pressure seal fora continuous pressure compartment.

Owing to Equation 8 of U.S. Pat. No. 5,282,384 a local fracturepropagation pressure maximum will correspond to a local porosity minimumwhich will usually coincide with a local intergranular permeabilityminimum. Both intergranular permeability and fracture permeability willusually be relatively low in the same place but for different reasons.Open fracture permeability is many orders of magnitude higher thanintergranular permeability for rocks that could form effective pressureseals. Fluid escape to the surface through fractures is many orders ofmagnitude easier than through the grains, so open fractures are theleast work path.

FIG. 2 shows a generic pressure compartment illustrating the additionalin situ corollary force balance inter-relationships which are part ofthis new method. The stippled area 15 between the two (2) fracturedshale beds 16 and 17 represents a continuous pressure compartment. Apressure compartment is a continuous rock body with sufficiently highpermeability to reach a seal relative hydrostatic condition. It can beany size or shape. It is defined by its static fluid pressure property,(i.e.) that pressure everywhere within the compartment is a relativefluid density-elevation relationship which can be calculated usingPascal's Principle. For example, a continuous rock body with anintergranular permeability above 10 millidarcies would equilibrate toseal relative hydrostatic pressure within several thousand years andthus be a pressure compartment.

Caprock seal fracture pressure when applied with Pascal's Principle isthe effective upper limit of the maximum pore pressure which can bereached anywhere within an underlying moderate to high permeabilitypressure compartment. Elevated pore pressure at the Minimum Work LeakPoint of the underlying continuous pressure compartment will openfractures in the overlying caprock seal at its fracture pressure andfluid will easily escape until the fractures close. This spatial in situfracture pressure/pore pressure force balance limiting relationship isgeneral and leads to a new method for forecasting pore pressure belowthe top petrophysical sensor of a Measurement-While-Drilling tool stringof the type known in the art based upon those sensor readings.

Inset circle 18 in the upper left of FIG. 2 represents a single verticalfracture perpendicular to the minimum principle stress within thecaprock 16. The opposing arrows in all three (3) inset circles 18, 19and 20 represent the minimum principal stress which has a magnitudeproportional to the effective vertical stress in ˜biaxial Normal FaultRegime basins. A tensile fracture with no shear offset will be closed ifthe pore fluid pressure within the fracture is less than or equal to thecaprock fracture pressure.

The Minimum Work Leak Point, illustrated in 19, for a pressurecompartment shown on FIG. 2 is just below the hydrocarbon water contact.If there are no hydrocarbons, and the caprock 16 has uniformpetrophysical properties, the caprock Minimum Work Leak Point is at thehighest elevation of the pressure compartment. The force balance at thepressure compartment--caprock interface changes systematically withoverburden and elevation in FIG. 2 as it does with any pressurecompartment.

The fluid pressure within the compartment changes in direct proportionto average fluid density/elevation (Pascal's Principle). For subsurfacebrines this fluid pressure gradient is somewhere between 0.434 to 0.507psi/foot. The change in fracture pressure with elevation is somewherewithin the range of 0.9 to 1.15 psi/foot. This force balancerelationship depends on caprock porosity, overburden and pore pressure.The compartment pore pressure limit is much more dependent on overburdenthan it is on caprock porosity.

Starting from the lowest caprock seal point of a continuous pressurecompartment and progressing upward, the sealing caprock fracturepressure decreases about twice as fast as the compartment pore pressure.A relatively uniform caprock 16 is about 0.5 psi easier to fracture witheach foot of gained elevation. The caprock Minimum Work Leak Point iswhere the compartment pore fluid pressure is highest with respect tofracture pressure in the overlying caprock. At that point, there are noadditional capillary forces to overcome to open a fracture if the fluidin the compartment and the fracture are equally wetting.

However, if the compartment pore fluid contains hydrocarbons and thefracture surfaces are water wet, a considerable additional capillaryresistance must be overcome for the two-phase fluid in the reservoir toenter the water wet fracture. The additional pressure needed to force atwo-phase fluid into a capillary size fracture is usually two times ormore greater than the single phase pore fluid entry pressure. In generalthe capillary entry pressure for a hydrocarbon increases much fasterthan the slight additional pressure resultant from hydrocarbon/waterdensity contrast. The increase in work required to force the two-phasefluid into the fracture is much greater than the slight decrease infracture pressure that accompanies the change in overburden andelevation.

The relevant force balance affecting pore pressure, fracture pressure,capillary pressure and overburden are covered in the discussion aboveand their approximate magnitudes quantified. Tensile fractures arepervasive in the subsurface particularly where pore pressures have beenelevated in the past. Considering all these together, the Minimum WorkLeak Point for the pressure compartment will normally be very near thehighest single-phase fluid elevation.

The above discussion omits the issue of compartment pressurecommunication through open faults. If an open fault cuts the pressurecompartment anywhere, top or side; the open fault is the minimum workcompartment pore pressure regulating mechanism. Open faults can onlylower the compartment pore pressure below that of the caprock MinimumWork Leak Point for the pressure compartment. Even a perfectly sealingfault cannot exceed this. In a geologically short time, minerals aredeposited in the open spaces within a fault zone. In the absence ofcontinued fault displacement, cement deposition lowers fracturepermeability gradually and returns the open fault to a closed sealingcondition. When fault sealing is complete, the Minimum Work Leak Pointagain becomes the continuous compartment pressure limit.

Though perhaps not immediately obvious from the above discussion,fracture pressure derived while drilling can be used as an effectivepore pressure limit predictor at or ahead of the bit. The drillingdecision of whether or not an additional casing string is requireddepends upon the maximum pore fluid pressure expected below. Drillingcan safely proceed through the underlying continuous pressurecompartment without setting casing if the maximum expected pore fluidpressure within the compartment is less than the minimum open holefracture propagation pressure.

The Measurement-While-Drilling petrophysical sensors, of the type knownin the art, on a typical drill collar are usually placed as close aspossible to the bit. This distance is often as little as twelve (12)feet. The increasing fluid pressure transition zone below a sealingcaprock 16 is usually tens to hundreds of feet thick. In the well beingdrilled, fluid pressures within a pressure compartment ahead of the bitvary according to Pascal's Principle. The geometry and continuity ofpressure compartments are known or inferred before an oilwell drillinglocation is selected. Garrenstroom et al in their 1993 article produceda map of the expected pressures and compartment lateral boundaries for alarge part of the Central North Sea. A new well is generally drilled tofind and produce hydrocarbons and there is an expected if not knownhydrocarbon water contact.

As the well is drilled, geologists keep track of bottom hole location,and the stratigraphic interval being penetrated. Drilling fluid densityis adjusted to be within a "Safe Drilling Window" which is defined bythe drilling fluid density range between the maximum open hole porepressure and the minimum open hole fracture pressure. It would beextremely valuable information if the driller could know the maximumpore pressure that can be expected before entering the next pressurecompartment below. Another casing string will be required if the maximumpore pressure in the underlying compartment is above the minimum openhole fracture pressure. The maximum fracture pressure at the MinimumWork Leak Point for the pressure compartment calculated in combinationwith Pascal's Principle is the pore fluid pressure limit for the entirecompartment.

FIG. 2 defines the unloading limb sealing mechanism as a relative forcebalance phenomenon. A local maximum fracture pressure can be definedfrom a continuous fracture pressure log. The trigger point-transitionfrom loading limb to unloading limb stress/strain relationships wouldnecessarily occur at some local fracture pressure maximum. A localfracture pressure maximum can be calculated directly from in situ straindata using a combination of Equations 7, 8, and 9 in U.S. Pat. No.5,282,384 to Holbrook.

The opening and closing of minimum work fractures in rocks is controlledby Equation 9 of U.S. Pat. No. 5,282,384 force balance. D'Arcie flow tothe surface operates independently of permeability type always followinga least work path. As the method for establishing the maximum pressuresealing efficiency point is coincident with the point of departure fromthe loading limb, it will be described in detail first.

FIG. 3, is a logical flowchart to identify pore pressure increasesassociated with possible local sealing fracture pressure maxima. FIG. 3describes a pair of binary decisions which, when executed with eachsuccessive True Vertical Depth (TVD) increment, will discriminatepossible higher fluid pressure sealing fracture pressure maxima fromthose which are not. FIG. 3 describes a computer algorithm, which can beexecuted using TVD data from either file input or real-time drilling.Operations START, Check for Exit, Data retrieval, and END are externalcomputer control operations which are not primary elements of thecompartment seal recognition process. Recognition of possible pressurecompartment seals is accomplished by the two decision diamonds 21 and 22portrayed executed in series as shown in the flowchart.

The first decision diamond 21, "Fracture pressure change over 5 feet",defines whether a fracture pressure maximum has been reached or not bycomparing successive values. If the estimated fracture pressure of thepresent point is greater than or equal to the last point, a locallydeepest fracture pressure high has not been reached. There is no reasonfor further seal evaluation in this case, so control is passed to the"save last pressure", process box 23 and the next successive TVD set ofdata points is retrieved for comparison.

Following retrieval of the next set of data points, the same decisiondiamond 21, "Fracture pressure change over 5 feet", is encounteredmaking the same decision on the next successive foot. This loopcontinues until the first falling fracture pressure data point isencountered. Dotted box 24 is on the logic flowpath, but is not aprocess. Box 24 indicates the fact that, "A possible sealing fracturepressure maximum has been penetrated". At this point the TVD set of datapoints is an unconfirmed candidate seal. But, the first short decisionloop alone has eliminated most data points from seal candidacy.

The next decision diamond 22 encountered on the "Less" side of the firstdecision diamond 21 is "Pore pressure gradient change from 5 feet aboveseal". Here the comparison is made between the slope (ΔPp/ΔTVD) ofsuccessive pore pressure estimates to determine if there has been anychange within or across the candidate seal. There are two (2) possiblealternatives of this binary comparison which are also shown on the logicflowpath in dotted outline boxes 25 and 26. Again these are not part ofthe process, but indicate the state of fracture pressure/pore pressurerelationships at that point in the logical flowpath.

If the pore pressure gradient is "Less than or equal to", the previousTVD pore pressure gradient; the "Previous fracture pressure maximum didnot cause an increase in pore pressure gradient", box 25, conditionexists. The existing pore pressure trend is no greater than that abovewhich may have been controlled by a loading limb stress/strainrelationship. Most local fracture pressure maxima have a pore pressuregradient below which is no higher than the pore pressure gradient above.These data points are also eliminated as candidate seal points and theprogram loops back up to retrieve the next successive TVD set of datapoints. The left, "equal or less" half of this decision flowchart willalways result in the elimination of a TVD dataset from candidacy as apossible unloading limb fracture pressure seal.

The only remaining possibility of this decision flowchart is that the,"Pore pressure gradient has increased under a possible fracture seal",box 26. This is a very important observation which triggers the next twoprocess control operations. If the "Greater than" condition is met inthe "Pore pressure gradient change from 5 feet above seal" decisiondiamond 21; the computer program or individual monitoring the changes indata should, "Save the last maximum fracture pressure, pore pressure,and TVD into a possible seal file", box 27. If these two (2) datacomparisons are made by a computer program, the next step 28 in theprocess is to, "Display the last possible unloading limb seal depth anda warning to a computer terminal".

Increasing pore pressure gradient below a candidate seal is indicativeof more dangerous drilling conditions below regardless of the fluidpressurization mechanism. The loading limb calculated pore pressure is aminimum expected pore pressure value for this TVD. From this pointonward pore fluid pressure will either increase at the effective stressloading limb rate or faster. If pore pressure under a possible fracturepressure seal is increasing at a faster than previous (ΔPp/ΔTVD) ratethe operator should consider fluid expansion unloading as a possibleadditional pressurization mechanism and act accordingly.

The above described flowchart eliminates over 99% of the total drilledfootage in any well from the candidate unloading limb fluid expansionpressurization category. The decision as to whether to shift to anunloading limb stress/strain relationship, and what that relationshipmost likely is should be made at this time.

The dual High Temperature, High Fracture Pressure conditions that leadto fluid expansion unloading are usually consistent within a local area.The methods of Bowers and Ward (1994) can identify the general areas anddepth ranges where fluid expansion has definitely forced the subsurfacestress/strain relationship onto the unloading limb. Their post factomethods of analysis also provide a reasonable estimate of the relativeslope of the in situ unloading limb stress/strain relationship within aregion and depth range.

The procedure described in FIG. 3 identifies which relative porosity lowand consequent fracture pressure high is the seal within the caprockcontaining possible fluid expansion pore pressure. If the candidateunloading limb fracture pressure TVD falls within a depth window roughlydefined by a Bowers or Ward method, the operator should seriouslyconsider switching to an unloading limb stress/strain relationship atthe most likely sealing point.

The methods for determining the maximum expected pore fluid pressurewithin an underlying continuous fluid pressure compartment, and a moreaccurate method for determining the slope of regional (ΔPp/ΔTVD)gradient using the same five (5) physical variables will be describedbelow.

FIG. 4 is a flowchart describing the fixed process steps which should betaken to calculate the maximum expected pore pressure (Ppmax) that wouldoccur anywhere within a continuous pressure compartment based upon anobserved caprock fracture pressure above the minimum work compartmentleak point (Pf@lp). FIG. 4 shows the procedure that corresponds to thegeneral caprock to compartment physical-spatial relationships shown inFIG. 2.

The stepwise procedure described in FIG. 4 can be applied every time onepenetrates an observed local fracture pressure maximum during thedrilling of a borehole into the Earth. Typically, the distance between afracture pressure maximum in a sealing caprock and an underlyingcontinuous pressure compartment is 50 feet to 500 feet. Typically, theoffset between the top petrophysical sensor in an MWD drillstring isless than 20 feet. The 30 feet plus margin is sufficient so that casingcan be set in the low permeability caprock before the drill bit actuallypenetrates into the potentially dangerous higher permeability continuousfluid pressure compartment. Casing cemented across the highest fracturepressure in the caprock will provide the maximum margin of safety wheninitially penetrating the underlying continuous pressure compartment.

There are two (2) basic steps in the procedure for calculating thepressure limit everywhere within a continuous pressure compartment shownon FIG. 4. The first basic step is to calculate the minimum work caprockfracture pressure for the underlying compartment. The first ten (10)process steps, 30 through 39, are surrounded with solid line boxes leadto the heavy line process box 40 where this calculation is made.

The second basic step which applies Pascal's Principle to calculate porepressure anywhere in the compartment has three (3) sub steps, 41, 42 and43, whose process box outlines are dashed lines leading to heavy lineprocess box 44. The fundamental process involves calculating the five(5) critical force balance variables from a measurement well profilepenetrating the continuous pressure compartment. The solid rock relatedforce balance variables, effective vertical and horizontal stresses areprojected from the Tangent Overburden gradient in the measurement wellprofile. These values are projected to the expected True Vertical Depthof the Caprock Fracture Pressure Maximum above the expectedhydrocarbon/water contact of the compartment. This provides aquantitative value for the force holding the pressure valve closedportrayed in the left blowup circle 19 on FIG. 2. Maximum fracturepressure at that Minimum Work Leak Point for the pressure compartmentsets the proportional limit for the entire compartment.

The static fluid pressure proportionality function is Pascal's Principlewhich is a simple linear function of elevation and average fluid density(ρ_(f)) from the Minimum Work Leak Point for the pressure compartment.Subsurface waters are very close in composition to Sodium Chloridebrines. The density of subsurface brines are often available from directfluid density measurements of water produced from nearby oilwells. Ifthese measurements are not available, the density of NaCl brines can becalculated with 0.01 g/cc accuracy from PVT-NaCl salinity relationships,as described in the 1987 article by Kemp.

The in situ density of oil and gas under various pressure, volume andtemperature (PVT) conditions is also routinely calculated for reservoirproduction purposes. Repeat formation pressure measurements arefrequently made within producing reservoirs to determine the in situformation water pressure gradients (wgrad); or the in situ partiallyhydrocarbon saturated fluid pressure gradients (dgrad) directly.

The uncertainty in fluid density plays a very small role in the overallcalculation scheme portrayed in FIG. 4. Fluids occupy only a smallvolume fraction in a sedimentary rock and fluid densities span a fairlynarrow range. The variability the in four (4) solid rock relatedpressure gradients is much more important to the outcome of the overallcalculation scheme. The selection of a good and representative tangentOverburden Gradient (step 32 of FIG. 4) is probably the most importantstep of the procedure from an overall quantitative output point of view.

The most significant factor affecting fluid expansion pressurization isthe regional geothermal gradient. Higher geothermal gradients lead togreater fluid expansion with depth and steeper unloading limb effectivestress relationships. Both the in situ loading and unloading limbstress/strain relationships are very steep. The loading limb effectivestress slope is 83.46 degrees for shale, 85.67 degrees for rounded purequartz sandstones and 85.66 degrees for rounded calcite grainstones.

The unloading limb effective stress/strain relationship for each ofthese minerals is steeper. At 90 degrees the stress/strain slope isundefined. The relative unloading limb stress/strain relationship iscalculated in degrees so that a change in the unloading factor (UNL₋₋FACT) will have a proportional change on calculated effective stress andpore pressure. The unloading limb factor is limited between 0.0 degreeswhich is coincident with the loading limb, and 4.19 degrees whichcoincides with the highest real number sigma max intercept which can bestored as a real number in a computer. Unloading factor values outsideof this range are not allowed. This computer memory upper limitcorresponds to a slope limit of 89.993 degrees which should not affectany real unloading limb calculations. The maximum expected real numberslope using known maximum sediment porosities is 89.86385 degrees.

Given a very high fracture pressure seal, the unloading limb factorseems to vary within a narrow range (˜0.02 ) degrees within an area ofseveral square miles. The unloading limb factor is consistently higherin higher geothermal gradient areas and lower in lower geothermalgradient areas. There is not much unloading limb data at this time andall of the unloading mechanisms are not sufficiently well understood togo further. What can be said is that if the procedure described in thefollowing flowchart is followed for several wells in a local area, thesame unloading limb factor produces equally good results in all localarea wells.

The method described in FIG. 5 involves a more precise physicallydescriptive identification of seal depth which can cause the onset offluid expansion unloading. In FIG. 5 the seal is identified andquantified by its high fracture pressure which is additional valuableinformation. The flowchart also provides a means for re-setting themineralogic unloading limbs in case the operator errs in placing theestimated seal depth too high. This feature makes the overall procedureuseful for real time drilling operations. The flowchart of FIG. 5encapsulates how, where, and why one would switch from loading tounloading stress/strain relationships for pore fluid pressurecalculations. The slope on the loading limb stress/strain relationshipsappear to be global constants which are only a function of averagesedimentary rock mineralogy as described in the 1995 article byHolbroolk. The slope of the unloading limb stress/strain relationship isrelated to regional geothermal gradient, and must be determined for thelocal region.

Referring to FIG. 5, therein is described the preferred procedure. InFIG. 5 there are four (4) decision diamonds 45, 48, 54 and 56 on theprogram flowchart. The first two 45 and 48 involve operator choices, thesecond two 54 and 56 are objective choices which can be made by acomputer based upon comparison of successive True Vertical Depth datavalues.

Steps 46 and 47 of the flowchart summarize the steps of calculating thecritical five (5) force balance variables from successive petrophysicalmeasurements. The method described by Holbrook, U.S. Pat. No. 5,282,384is preferred, but any other procedure for acquiring the same five (5)force balance variables is not excluded.

The program operator must set the program onto the unloading limb at adepth based upon local experience in a given area 48. The preferreddepth should correspond to a high fracture pressure seal. These sealsare usually related to stratigraphic depth, but continuous diageneticseals have also been suggested. At the expected onset of fluidpressurization unloading, the operator turns on an unloading limbcalculation switch 48 which leads to the next lower part of the programflowchart. The operator also provides at this time, the unloading limbfactor which is the number of degrees between the loading and unloadinglimbs in the local area 49.

The depth of a fracture pressure high in the probable seal isresponsible for containment of fluid expansion pore pressure. The powerlaw linear loading and unloading limbs intersect at that point. Theporosity, mineralogy, and force balance variables at that depth aretransferred to solve for the slope and intercept of the unloading limbgiven the unloading limb factor, step 50.

The unloading stress/strain (solidity) slopes for each end membermineral are preceded with "UNL₋₋ A₋₋ ", with the described mineraldescriptor attached, step 51. The stress/strain solidity=1.0 interceptof the power law function for each end member mineral are all labeledwith the prefix, "UNL₋₋ Smax₋₋ ", with the described mineral descriptorattached. The program reserves a low and high "UNL₋₋ Smax₋₋ " memorylocation which are set to the same value at 52. The high and low memorylocations will be used subsequently if the operator has made anincorrect estimation anticipating the peals fracture pressure.

A peak, thermal expansion fluid pressure "Pth", is calculated from theaverage Geothermal gradient of the area, step 53. The average geothermalgradient is supplied by the operator, step 46. The depth differencebetween the "TVD Seal", and the present "TVD" depth of a sample providesthe temperature difference needed for the calculation. The thermalexpansion coefficient "Texp", for a Sodium Chloride brine under theexisting pressure temperature conditions is used.

Following this step the program makes a data comparison 54, to determineif the fracture pressure at the present TVD is greater than the previousmaximum fracture pressure "Pf max", which is held in computer memory. Ifthe fracture pressure is less than "Pf max", there is probably no changein the unloading limb status. If on the other hand, fracture pressurehas increased above the previous maximum, "Pf max", and "TVD Seal" arereset to the new higher values, step 55.

In either case the program proceeds to the next decision diamond 56, ie."Is "Solidity" greater than the previous Solidity max", which is held incomputer memory. Again if "Solidity" is less than the previous "Soliditymax", the present mineralogic unloading limb slopes "UNL₋₋ A₋₋ ", andstress/strain solidity=1.0 intercept, "UNL₋₋ Smax₋₋ ", are stillappropriate for calculating Pore Pressure from Effective stress andstrain (Solidity), step 57.

If however, "Solidity" has increased above the previous "Solidity max",which is held in computer memory, the peal, sealing fracture pressurehas not been reached. This is the "Yes" exit to the decision trianglewhich leads to a different calculation procedure for pore pressure "Pp",and a re-setting of the unloading limb stress/strain coefficients "UNL₋₋A₋₋ ", and "UNL₋₋ Smax₋₋ ", effect is accomplished as shown in theprocess block 58, which is repeated for each mineralogic end member.Process block 58 corrects the unloading limb to account for the higherthan expected seal fracture pressure "Pf" which will be applied to thenext calculation.

Effective stress "Est" is calculated from the old "Smax" set ofcoefficients, step 59. There probably was some increment of thermalexpansion since the last estimated seal depth in this case. Thatincrement of additional pore pressure "Pth" is then added in the nextprocess calculation 60.

A final pore pressure comparison 61 is made to determine if thecalculated pore fluid pressure gradient, "Pp" has exceeded the previousmaximum fracture pressure gradient "Pf max" which was held in computermemory. If so, then the calculated pore pressure is reduced to thatfracture pressure gradient. This is the theoretical force balance limitif the fluid contained in the pressure compartment is water.

The program then displays and stores all calculated force balancevariables and cycles back to gather more petrophysical data. This isportrayed by the return looping arrow 62 on FIG. 5. This step isexecuted in the same manner whether on the loading or unloading limb.The process continues until the program either runs out of data or isterminated by the operator. The overall process described in thispreferred embodiment has described a method wherein an operator cancalculate pore fluid pressure using mechanically sound force balancerelationships using appropriate physical constraints whether thepressure driving mechanism is disequilibrium compaction or unloadingfluid expansion.

The foregoing disclosure and description of the invention isillustrative and explanatory thereof, and various changes in the methodsand techniques described therein may be made within the scope of theappended claims without departing from the spirit of the invention.

What is claimed is:
 1. A method for determining pore pressure in asedimentary rock at locations in a subsurface formation penetrated by aborehole, comprising the steps of:determining the loading limbstress/strain relationship for said sedimentary rock using a forcedbalanced stress/strain relationship; estimating the slope of theunloading limb stress/strain relationship for said sedimentary rock at afirst location depth in said borehole using a forced balancedstress/strain relationship; determining the intersection point of saidestimated unloading limb stress/strain relationship with said loadinglimb stress/strain relationship; determining the unloading limbstress/strain relationship for said sedimentary rock from said estimatedslope and intersection point; and determining from said unloading limbstress/strain relationship the pore pressure of said sedimentary rock atmultiple locations of said borehole.
 2. The method of claim 1 furthercomprising the steps of:determining the pore pressure in saidsedimentary rock from said loading limb stress/strain relationship; andswitching from said loading limb stress/strain relationship to saidunloading limb stress/strain relationship to determine pore pressure forsaid sedimentary rock.
 3. The method of claim 1 wherein said step ofdetermining the unloading limb stress/strain relationship in asedimentary rock penetrated by a borehole, comprising the stepsof:determining the strain for said sedimentary rock; determining theeffective stress for said sedimentary rock; and determining theunloading limb stress/strain relationship from said strain and saideffective stress for said sedimentary rock.
 4. The method of claim 3wherein the step of determining the strain of said sedimentary rockcomprises the relationship (1.0-φ), where φ is porosity for saidsedimentary rock.
 5. The method of claim 3 wherein the step ofdetermining the strain of said sedimentary rock comprises therelationship (φ/1.0-φ),where φ is porosity for said sedimentary rock. 6.The method of claim 3 wherein the step of determining the effectivestress for said sedimentary rock comprises the steps of:determining theoverburden for said sedimentary rock at said first depth location ofsaid borehole; determining the pore pressure for said sedimentary rockat said first depth location of said borehole; and determining theeffective pressure, for said sedimentary rock from said overburden andsaid pore pressure.
 7. The method of claim 1 wherein the step ofdetermining the loading limb stress/strain relationship furthercomprises the steps of:determining the overburden of said sedimentaryrock at said first depth location of said borehole; determining theeffective stress at each of a multiple of incremental depth locations ofsaid borehole; determining the solidity of said sedimentary rocks ateach of said multiple of incremental depth locations of said borehole;determining mineralogy of said sedimentary rocks; and determining saidforced balanced stress/strain relationship for said loading limb.
 8. Themethod of claim 7 wherein the step of determining the unloading limbstress/strain relationship further comprises the steps of:determiningthe overburden of said sedimentary rock at said first depth of saidborehole; determining the effective stress at each of a multiple ofincremental depth locations of said borehole; determining the solidityof said sedimentary rocks at each of said multiple of incremental depthlocations of said borehole; determining mineralogy of said sedimentaryrocks; and determining said forced balanced stress/strain relationshipfor said unloading limb.
 9. The method of claim 8 wherein said forcedbalanced stress/strain relationship for said unloading limb is derivedfrom local geologic conditions.